There are several ways to look at the absolute value concept. One way is to consider the absolute value as the
from the center of the number line to a given point. The center of the number line is the number
. Since distance is always positive, we report the distance from zero to any point as a
number. When asked what is the distance from Chicago to St.
Louis, you don't hear people say several hundred negative miles, do you? So
How "far" is it from 0 to the number 15? Answer: 15 units
How "far" is it from 0 to the number -15? Answer: 15 units
Using the absolute value notation:
This leads into another way of looking at absolute values.
The absolute value is a
You put a number into it, and the number pops out
If x is a negative number, change the sign of x and write the result.
If x is a positive number, don't change its sign. Write it as it is.
Change the sign of -15 and write the result: 15.
There is no need to change the sign. Just write the number 15.
The way we write "x is a negative number" is like this : x < 0.
"x is positive" is written as x > 0. If we include zero here, we write x > 0.
Hence, we can write the absolute value function like this:
It still works the same way as before, if x is a negative number, change its sign. Don't change the sign if x is positive.